GPM is short for gold per minute. It is the average amount of gold a hero earns per minute of the game. The stat is shown on the post-match scoreboard, in the player profile, and on external stats services, and in discussions it is almost always placed next to XPM, experience per minute.
What makes up GPM
Gold in Dota 2 comes from several sources: last-hitting enemy creeps (neutral and lane creeps), killing heroes and assisting in kills, destroying buildings, and the base passive income that all players receive. The more efficiently a hero farms and the more often they take part in successful fights, the higher their GPM. Lost gold, for example from dying, also affects the overall picture.
How to read the number
The main rule: GPM should not be judged in a vacuum. A carry usually ends up with the highest value, because the team is built around their farm. A support's GPM, as a rule, is noticeably lower: their job is not to accumulate gold, but to spend resources on vision, consumables, and helping teammates. That is why comparing the numbers of players in different positions is meaningless. It makes sense to compare a hero with players in the same role and at the same skill level.
In addition, GPM is an average over the whole match. It smooths out fluctuations: a player might have had a weak first half and picked up speed toward the end, and the final number will not show that. For analyzing a game, it is more useful to look at the gold graph over time than at a single number.
A typical situation
Suppose that after a game you see that your carry's GPM is noticeably lower than usual on that hero. Possible causes: frequent deaths in the lane, poor use of jungle camps, a long road to the first key items, constant fighting without farming. Reviewing the replay helps you understand what exactly fell short: lane control, routing around the map, or decisions in fights.
Limitations of the metric
A high GPM does not guarantee a win. You can collect a lot of gold and still lose if it doesn't turn into map pressure, taken buildings, and won fights. Conversely, a team can win with modest numbers if it makes good use of its advantage. GPM is a convenient indicator of the economy, but not an assessment of a player's entire contribution. It should be used together with other stats, such as KDA, and with an overall understanding of how the match unfolded.