Furtka jest obok bramy, więc wchodzimy tędy pieszo.

Furtka is a small gate, usually for people walking through.

Brama is a large gate or main gate, often big enough for cars or other vehicles.

So in this sentence, the idea is:

• there is a small pedestrian gate
• next to a larger main gate
• and because of that, we go in through the small gate on foot

Because obok normally requires the genitive case in Polish.

• nominative: brama
• genitive: bramy

So:

• obok bramy = next to the gate

This is a very common pattern:

• obok domu = next to the house
• obok sklepu = next to the shop
• obok szkoły = next to the school

Furtka is in the nominative case, because it is the subject of the sentence.

In Furtka jest obok bramy:

• furtka = the thing being talked about
• jest = is
• obok bramy = next to the gate

So furtka stays in the basic dictionary form here.