The apostles had fulfilled the mission on which Jesus had sent them (cf. 6:7ff). They returned to Jesus to give Him a report of their good works and teachings.
Jesus then encouraged them to come with Him for a period of rest where they could be alone. It appears that their work in the cities of Galilee was highly successful due to the amount of people who were coming to them at this time. They were so busy they didn't even have time to eat! The people were evidently making so many requests for healing and teaching that it was almost overwhelming. Jesus and the apostles intend to get some rest by departing by boat to be alone.
There is a valuable lesson that should be gleaned from this passage. It is proper for followers of Christ to take brief periods of rest from hard and continuous labor in His kingdom. It is good to rest periodically and simply get away from the rapid pace of life. In order to do this, it is sometimes necessary for us to say "no" to certain requests and opportunities to serve. This is not wrong. Of course, it is possible to have too much rest and leisure, and this is not good, just as it is not wise to constantly labor without ever resting. The former will generally lead to poor stewardship and entanglement in sin and the latter will often lead to burn out and discouragement. Jesus invited His apostles to rest a while. In other words, the rest would not go on for a long span of time. They would rest for a while and then get back to work.
Christians must seek the proper balance in this area, and such will be different for each individual. Some disciples require less sleep than others and are able to work diligently in God's kingdom with little rest. They are able to stay focused for long spans of time and are generally not subject to discouragement. Others, however, need more frequent periods of rest to remain positive and focused. God has blessed different servants of His in different ways (cf. Matt. 25:15), and it is not our duty to judge our brother regarding the amount of rest and relaxation he may or may not require (cf. Rom. 14:10-13). It is our duty, however, to encourage one another to faithful living to the best of our ability, including resting and recharging as needed. A servant who rests continually will not be of any use to the Master. Likewise, a servant who works so hard that he neglects himself (or his family) will certainly not maximize his potential for the Lord.
As a side note in the context of Mark 6, it is quite possible that the disciples were not simply getting away to rest from their physical labors and travels. It would appear that they had just learned of John the baptizer's death (cf. Matt. 14:13). Certainly there would be much excitement stirred up by this event (as Herod had originally feared), and it is very likely that John's disciples delivered the message to Jesus with the expectation that He do something about John's wrongful death. The people knew that Jesus was a friend of John and that He intended to set up a kingdom. They also believed (mistakenly) that this would involve overthrowing Herod. They appear to be more than willing to revolt and make Jesus their physical king with the hopes of obtaining revenge (cf. John 6:1,2,15). Jesus had no intentions of establishing a physical kingdom. Thus, it was wise to seek to be alone for rest from their labors, to mourn John's death, and to calm the people.
Dear friends, may we work diligently for the Lord and rest when we need to. May we never forget that there remains "a rest for the people of God"--the glory of heaven (Heb. 4:9), which is a much better rest than anything we can enjoy in this life.