The web spell's effect can render some creatures entangled, a condition which can make casting spells and attacking difficult:
The character is ensnared. Being entangled impedes movement, but does not entirely prevent it unless the bonds are anchored to an immobile object or tethered by an opposing force. An entangled creature moves at half speed, cannot run or charge, and takes a -2 penalty on all attack rolls and a -4 penalty to Dexterity. An entangled character who attempts to cast a spell must make a Concentration check (DC 15 + the spell’s level) or lose the spell.
Emphasis mine. Otherwise, a creature's casting and attacks are unimpaired by the web spell's effect. However, creatures with the web spell's effect between them may find combat and spell targeting difficult:
If you have at least 5 feet of web between you and an opponent, it provides cover. If you have at least 20 feet of web between you, it provides total cover.
Any cover prevents attacks of opportunity, for instance. And total cover blocks line of effect, which most folks need to do pretty much anything to anyone.
A quick note on the web spell's effect
The spell web does not create a lone, giant spider's web that essentially renders creatures that fail the saving throw helpless like a spider's web does its prey but creates, instead, a wall-like mass of web-like strands that creatures can try to push their way through. The effect can secure unlucky, weaker creatures in their spaces, but those creatures are still capable of exerting force and struggling against the strands—and, with difficulty, making attacks and casting spells. So while the spell says, "These strands trap those caught in them," first it says, "Web creates a many-layered mass of strong, sticky strands." How the effect traps affected creatures is governed by the condition entangled and the remainder of the spell's description.