In General
The precepts of the church are five extra obligations which are binding on Catholics. The Ten Commandments are applicable to everyone in the world, no matter what religion. Even if they don't know about the Ten Commandments, they are still applicable. These five precepts of the Catholic Church are further obligations for Catholics to fulfill. They pertain to particularly Catholic practices, so they are really only binding on Catholics. Of course the Catholic church wishes everyone to be Catholic, so it wishes everyone to be bound by these, but if someone is not a part of the Church for whatever reason, they would not be obligated to fulfill these. These precepts are minimum practices which Catholics should partake in in order to remain in the state of grace. Fortunately, most practicing Catholics do much more than these bare minimums, but it is still important to be aware of them.
Attend Mass on Holy Days of Obligation and Sundays and abstain from servile labor
This is really just an extension of the Third Commandment, Keep Holy the Lord's Day. God gives us this commandment in very general terms, to abstain from work on the sabbath and to worship God. The Church just clarifies this commandment to positively command the faithful to attend mass. As the highest form of prayer and worship, attending Mass at least on Sundays and Holy Days of Obligation is the best way to worship God and fulfill the third commandment. This is a positive obligation enjoined on us by the Church who has, in her wisdom, decided that attending mass is the best way for Catholics to worship God. When we attend mass on this regular basis, we glorify God by worshiping Him and showing Him our great love for Him.
Confess Sins at least once per year
This particularly applies to mortal sin. It is good to keep in mind that these precepts are a bare minimum. Hopefully every Catholic goes to confession frequently, and tries to get to confession as soon as possible if they have committed a mortal sin. With this precept, the Church is telling the faithful that confession is important and that it must be done on a somewhat regular basis. It is true that once per year isn't that regular, but this is just a minimum and a guide. The Church wants to make sure that everyone is going to confession at least somewhat, particularly if they have committed mortal sin. This precept should encourage us to partake of the graces of confession regularly, and much more than once per year.
Receive the Eucharist at least during the Easter Season
Again, this precept is dealing with a minimum requirement. The Church obviously encourages the faithful to receive Communion at least every Sunday, and if possible every day. This is such a great source of grace, and so it should be utilized as much as possible. It is extremely fitting to receive the Eucharist particularly during the Easter season because that is the time when we commemorate the death and resurrection of Jesus. He instituted the Eucharist on Holy Thursday, and the Eucharist is a remembrance and participation in the death and resurrection of Jesus. By mandating that Catholics receive communion during this holiest time of the year, the Church is highlighting the importance of this time of year and the importance of receiving the Eucharist.
Observe the prescribed days of Fasting and Abstinence
Fasting is an ancient practice of mortification, dating from the days of the Old Testament. In fasting, the person does not eat as much food in order to remind oneself about God and concentrate on loving God alone. Abstinence is defined as not eating the flesh of animals. It is permissible to eat fish on days of abstinence. This is a smaller sacrifice than fasting, but a sacrifice again to take the emphasis off food and concentrate on God. The Church has prescribed certain days of the year as days of fast and/or abstinence. These primarily fall during Lent. This precept exists to remind the faithful that the Church mandates these penances on the prescribed days. Each person is encouraged to sacrifice and pray on their own, but the Church has determined that fasting and abstinence is a sacrifice worth making for every Catholic.
Help Provide for the Needs of the Church
The Church has many needs, just like every organization. On a basic level it needs some money to keep things running, but it also needs people to help minister to the world. This precept of the church reminds us that as members of the Church, we have an obligation to help provide for its upkeep. This could mean contributing financially to help care for the financial needs of the church, but it also means volunteering or other personal service. There are many aspects of the church and its ministries which don't need money but do need people. We can contribute to the church by our presence and active participation in the life of the church.