Gravimetric analysis is the determination of the concentration, or composition of a compound according to it's weight, or a change in its weight.
One type of gravimetric analysis involves selectively precipitating the species that you want to analyse out of solution, leaving the other constituents there, then filtering and drying the precipitate. The weight of the precipitate can tell you how much of that species was in solution. (Some examples include precipitation of barium with a sulfate solution, calcium with a carbonate solution and nickel with a dimethylglyoxime solution)
This analysis is useful only if the analyte forms an insoluble precipitate, and if there are no other species which will react with that particular solution.
Another type of gravimetric analysis is to heat the sample to get it to release a gas. Heating sodium bicarbonate so that it releases carbon dioxide and leaves sodium carbonate is an example of this which is used in teaching laboratories to demostrate this principle.
Reacting the sample with a chemical which will dissolve or release a species is another type of gravimetric analysis. An example is reacting a carbonate containing mineral sample with an acid, letting the carbon dioxide escape, and then titrating the acid that's left with a base to find out how many moles of gas were evolved.
The limit to how accurate these methods are involves how close the reaction or precipitation goes to completion. A precipitate must be very insoluble in the solvent, stable to oven drying, and must go to completion in a reasonable amount of time. Losses of precipitate in transfer from one vessel to another must be avoided. The advantage to these methods is that the only expensive piece of equipment you need is an analytical balance.