1. Is it in the Bible?
No. (not in english--however the Greek word for "people" is "laos"--perhaps the origin of the term?)
2. What do we believe it means?
Lay people are the vast majority of church members who do not have a ministry or are not ministers in the church.
3. What does it really mean?
The term "lay people" is not at all in the new testament Bible. We might infer that it is in the old testament, since in the old covenant only the Levitical tribe was allowed to minister in the temple (once again we expose the old covenant typologies that operate our idea of "church")
Once can "read in" the concept of lay people into the new testament by a handful of references to "the people"
By the way the Bible is translated (and reading from our experience again!) some believe that the early church consisted of a "ministerial leadership group" of apostles and all else in the church were "lay people". this ignores the fact that the Bible says they were many moving in he prophetic gift and people were being added daily to the church. Nowhere does it say all this work was accomplished or "overseen" by the apostles. something that is missed is the disobedience of the early church. Jesus had commanded them to go outside of Israel with the gospel....
8 But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth. (Acts 1:8)
But they did not.
Since an "apostle: is "someone who is sent" the disobedience of the early church was not "sending" those whom God might choose to be sent with the gospel (apostles) outside the boundaries of Israel. Eventually, the entire church was run out of Jerusalem and finally did begin to carry the gospel out to the world.
Tradition has handed us a disobedient (ministry limited) church system, and we verify it by reading our experience of disobedience into the disobedient church!
There are no such thing as "lay people". All believers
have a ministry to fulfill for the Lord.