Question: What is the meaning of ''one block into'' in the below sentences? Which grammar rule ?

**You own a house one block into the ward.**

Answer: 
In the context of housing, a ***block*** is either a single (multi-storey) building containing multiple apartments / offices / etc., or a (usually rectangular) area between two pairs of intersecting roads, mostly or completely filled with buildings (houses / offices / shops / etc.).

And a ***ward*** usually refers to a residential area that's significant in the context of elections (all the voters who live in one ward get to decide who they will elect as their local councilor, for example).

I don't know the exact context of OP's example, but basically it means the addressee's house isn't on the very *edge* of a ward - there's one more block between his house and the one that's right on the electoral boundary (but considered to be *within* the ward).

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Syntactically, it's the same general construction as...

> 
> *I'm three weeks into my new job*
> 
> 
> 

...meaning *I started my new job three weeks ago.*
I believe it means *on the fringe of a district.* The word *ward* means *an administrative division of a city*. I believe it means that the person doesn't live in the center of the ward but somewhere at the margins.