What do Christians mean when they say God told them to do this or that?

We have communication with the Lord by the love of the Holy Spirit.

They don't want to take responsibility.

They do what they want, then convince themselves that God told them to do it. Look at all the different people God told to run for the same office.

They mean they have orders from their preacher.

The truth is that they either have a psychological problem where they are hearing voices (e.g. GN), or are lying (i.e. "prophesying" out of their own imagination; Ezk 13:17; probably also GN).  Here's how we know.

Ex 3:16 “Go, assemble the elders of Israel and say to them, ..." ... 4:1 Moses answered, “What if they do not believe me or listen to me and say, ‘The Lord did not appear to you’?” 2 Then the Lord said to him, “What is that in your hand?” “A staff,” he replied.  3 The Lord said, “Throw it on the ground.”  Moses threw it on the ground and it became a snake, and he ran from it.

When God spoke to people, he didn't expect others to believe them just because they said God spoke to them.  He gave them "horsepower".  He made it where listeners could confirm that their words were from God by giving them miraculous signs to perform (Jn 3:2; Mk 16:20; Heb 2:3-4).  That's one of many reasons why for example we know that Mo was a false prophet.  He even admits in his Koran that he had no miraculous signs to offer.

So if someone tells you that God told them this or that, ask them, "Other than just your word, how am I supposed to know if God really did speak to you?  God gave Moses miraculous signs so that others knew that God had spoken to him, what do you have to offer?"  If you really want to see them squirm, continue on with this: "Jesus said that one of the miraculous signs used to confirm his word was the ability to drink any poison without it harming them.  Can you drink a bottle of Clorox bleach without it harming you?"

The truth is that God's word as confirmed centuries ago, and as predicted by the apostle Paul, all that prophecy stuff ended just as the NT was finalized (1Cor 13:8-10).  So there is no more "God told me this or that".

Now that's not to say that certain things can happen in a Christian's life where they think that God may be leading them this way or that way, but it's always just an opinion.

When we ask God for His guidance in a particular situation, He offers it to us, sometimes through other people, or circumstances, or just suddenly making it clear which is the best way to proceed.

I've never, ever heard words from God in my ear, or in my head. But I have discerned God's will for me after praying about a matter, checking the Bible, praying a lot more and not stopping the search till the right thing to do became clear. On occasion I've opened the Bible and my eyes would fall on particular verses that sorted the problem out for me. Other times I would just feel so disturbed, unsettled, until I resolved to do what I knew was the right thing to do, even though I was reluctant, and straight away I'd get that peace in my soul which is the hallmark of the Holy Spirit's activity. It's all about sensitivity to the Spirit of God, which always aligns with his written word, the Bible, and a conscience that has been cleansed of sin.

Some claim they literally hear the voice of God. As everyone knows, hearing voices is a clear symptom of schizophrenia. 

Some claim they randomly hit on Bible passages and interpret that as God talking to them. Some interpret random events, phrases, road signs, etc., as the voice of God. Equally mental, IMHO. 

they mean to say that I want to do this or that

THEY MEAN WHAT THEY SAID....HE SPEAKS IN WHISPERS TO THE SAVED.