가능 means something is possible, that it can be done. It is a noun that can make other compound nouns (가능성 = possibility, 불가능 = impossibility) or adjectives (가능한, 가능하다). Your sentence can be interpreted like this. "휠체어 출입 가능 출입구는 Gate 7이에요." == 휠체어의 출입이 가능한 출입구는 7번 게이트예요. => (lit.) The entrance that a wheelchair can(가능하다) go through (출입하다) is Gate number 7. => The wheelchair-accessible entrance is Gate number 7. In Korean, simple phrases tend to contract to the shortest possible form when they become a part of a larger phrase. When 휠체어의 출입이 가능하다 takes on an adjectival function as here, the particles 의 and 이 as well as the adjectivizing ending 한 of 가능한 are dropped because the meaning is still clear even without them. So 휠체어의 출입이 가능한 shortens to 휠체어 출입 가능 to modify 출입구(entrance, gate), but the original long form is also okay to use when brevity is not the overriding concern.

In this sentence, there may are several gates. Some gates are too narrow, has stair or raised spot so wheelchair can't go inside. He is letting him know that gate number7 is clear to wheelchair can go inside.

Thanks Julie! I had a feeling it meant that, but now I don't understand why you would use "possiblility" in this sentence. Can you explain?

가능 means POSSIBLE. 휠체어 wheelchair 출입 Entrance 가능 possible, possibility, feasible 휠체어 출입 가능 : wheelchair entrance possible = wheelchair access