A foam mattress contains no pocket springs. It will either feature a denser foam base layer topped by a more cushioned foam upper, or it may have the addition of a memory foam top layer.
Generally, a foam mattress will be the cheapest mattress you can buy. They tend to be best for lighter-weight sleepers due to the lack of spring support, and they'll suit a side sleeper best as front and back sleepers may find the foam sinks too much for comfort.
If you struggle with mobility you might also find an all foam mattress difficult to get out of and turn over in as there's little to no bounce without those springs. Edge support can also be poor, so sitting on the edge of the mattress you'll sink rather than having a firmer surface to stand up from. That sink-in factor is good news for motion isolation though, with the all foam construction dampening the movements of any sleep partners for a less disturbed sleep.
In general, a foam mattress is unlikely to last quite as long as a mattress that has pocket-spring support, and you're more likely to find the sleep surface forms dips over long-term use.