What do Christians mean when they say they heard the Lord speak to them about something?
Most Christians who say that the Lord "told" them something do not mean that they heard an audible voice. Instead, they mean that they "heard" God "speaking" to their innermost being—impressing them about something. He does this through His Holy Spirit who dwells within the heart of every true believer. The Holy Spirit is our Guide and our Teacher, directing us to do what God wants us to do—God's will.
The Bible, God's love letter to us, is the primary instrument that God uses to "speak" to us. For example, you might read a verse in the Bible that seems like it was written just for you and your particular situation that day. Or, the pastor's message from the Bible may suddenly grip you in a special way. But the Holy Spirit will "speak" to you at other times and in other situations as well. He will let you know when you have done something wrong, or bring to mind someone to pray for, or give you peace (or lack of peace) about a certain decision, etc.
When you pray, ask God to give you sensitivity to His Holy Spirit, so that you will be alert to the many ways that He "speaks" to you throughout each day. However, remember that what you "hear" from the Lord must always agree with what the Bible teaches. Otherwise, it is not a word from God.