Jennie, for most of the last 800 years, the general practice of the Catholic Church in the west has been to distribute communion only under the species of bread. The custom took hold in part because the Church believes that Christ is entirely present in either species, but mostly because of reverence for the Eucharist which can easily be spilled when distributed to large numbers of people under the species of wine.
In the 1400, a group of people called “Utraquists” (from the Latin word for “both”) insisted that communion was only valid when one received under BOTH the forms of bread and wine, but the Catholic Church rejected this view as being heretical and wrong. As a result, it became the custom that the chalice was never offered to the laity, in order to emphasize that communion was complete under the species of bread alone.
After the Second Vatican Council in the 1960s, increased permission was given to priests to distribute communion under both kinds. However, the caution was given that the chalice should not be given if there were a likelihood that it might be profaned. Thus, while in some parishes you will find the chalice offered to the laity at all masses, at other parishes the priests may be more cautious, and limit communion under both kinds to major feast days, or perhaps never distribute under both kinds at all. However, always remember that whether you receive under only one species or under two, the sacrament is complete in either form, and those who receive communion as both bread and wine do not receive “more Jesus”, or get more grace, than those who receive under the form of bread only.