GDP is a measure of new value created in the system. It is a flow magnitude. That statement is supposed to convey the notion of it adding something new to something else that is already there ie to a stock of already present values. When GDP grows, the economy is expanding its value stock.
'Value', as it were, is composed of two constituent parts; there is a part related to price and a part related to quantity. Also, note that value should be treated as a plural form, in the sense that, there are a lot of things of value; the sum of those values is what constitutes the total value available at a point in time, for a given economy.
Treating GDP as a sum of values, allows us to decompose the change to its magnitude:
$ΔY = ΔY_1 + ΔY_2 + ... + ΔY_n$
(obviously, $Y$ denotes (the value of) GDP while $Y_i$ denotes the value of GDP's component $i$)
Further decomposition of the change in the $Y_i$'s yields:
From a first glance to the change formula shown above, one should notice that the total change for every value component of GDP ($Y_i$), can be attributed either to a change in price ($ΔP_i>0$) or to a change in quantity ($ΔQ_i$>0) or to a change in both ($ΔP_i>0$ and $ΔQ_i>0$).
When only the price changes, for a single component ie when $ΔP_i>0$ and $ΔQ_i=0$, a change in the value of that component is effectively an inflationary change. On the other hand, when the value of a component changes due to changes in the underlying quantity ie when when $ΔP_i=0$ and $ΔQ_i>0$, we get a real growth effect.
There are a few things to notice in this simple accounting exercise. The first has to do with the signs of the changes we are considering so far. Although we have talked about positive changes in either the price component or the quantity component, there is really no reason not to consider the case where these changes are actually negative.
A negative change in the price part is equivalent to valuing the same quantity (assuming $ΔQ_i=0$) of component $i$ for less. Similarly, when the quantity of component $i$ drops (assuming $ΔP_i=0$), there is less of the actual commodity or service $i$ available-in this sense, the economy is poorer in real terms. In the former case, the economy was simply cheaper as far as the $i$ component was concerned.
Another thing to consider, regarding the exposition so far, is that what happens to the value of component $i$ (whether it increases, decreases or stays the same) is not disconnected from what happens to the rest of the components of GDP. This means that frequently (but not always) it is the case that positive or negative changes in the price or quantity components of some of the constituent parts of GDP is accompanied by similar movements in the value of most other components of GDP.
Effectively, that means that changes in GDP ($ΔY$) are not happening because a few components suddenly jumped/dropped in price or quantity terms ($ΔP_i>0$ and/or $ΔQ_i>0$ for few $i$'s) at the same time. Persistent changes in GDP are due to persistent changes in most, if not all, the constituent components.
One more thing to consider is the fact that, most of the time, the parts that change are neither prices nor quantities in isolation but both of them in tandem. That poses the very real problem of distinguishing which part of the newly created value (GDP) is due to the economy having more of some commodities or services ($ΔQ_i>0$ for some $i$'s) and which part is due to price changes ($ΔP_j>0$ for some $j$'s). Note that in all likelihood some of the $i$'s and $j$ are the same. It is because of this eventuality that we make the distinction between real and nominal GDP. Real growth is related to increases in the available quantities of commodities and services while nominal growth might be underlined by inflationary pressures.
A final point to consider is that $ΔY$ ie the change in the value of GDP can come from another direction. Until now, we were considering the changes that were related to components $Y_i$ where $i=1,2,...,n$. Well, it so happens that $n$ is not constant but changes with time.
For some periods of time the number of available commodities and services might be equal to $n_1$ while for other periods the value of $n$ may be equal to $n_2$ and still other times it might be equal to $n_3$. What is important to understand is that it could be the case that $n_1<n_2<n_3$ but that is not necessary how they should rank. It is just the case that when $n$ increases, the value of GDP increases also and vice-versa (obviously, there is a ceteris paribus clause of constant prices and quantities for all the 'old' commodities and services).
When GDP changes in that manner, the change can be attributed to the introduction of new commodities and services. Generally speaking, when talking about GDP growth, what is tacitly understood is that $n=const$. The introduction of new commodities and services is generally attributed to the effects of technological change.
'Technological change' in economics is an all encompassing notion that fuses scientific progress with managerial and organizational changes in the way-of-doing-business. In that sense, the change in GDP that is attributed to technological change (what is frequently dubbed total factor productivity increases) might be due to the introduction of new commodities or services or the introduction of a better way of doing business but it might also be attributed to relative price changes due to innovations that conserve on (relatively) scarce productive resources.
Innovations that change relative prices effectively act upon the cost structure of some productive processes and if they are too disruptive they can also change the relative income distribution of the affected factors of production. These effects mean that innovations might lower the price component of (some) $Y_i$'s but it is not clear what will happen to the quantity component of those
$Y_i$'s (we abstract from any substitution and/or complementary effects between $Y_i$'s).
Having covered all this ground, we can say that economies grow in real terms when, on average, modest price increases are accompanied by strong quantity increases. Also, these movements should be such for the majority of commodities and services. Additionally, growth can come in the form of changing the cost structure of available production processes without causing incommensurate income disruption or, ultimately, from the expansion of the number of available commodities and services.