There are two main reasons why we call them pillars. The first is that they are arkaan (pillars), which is a technical term in the science of deriving law (usool-ul-fiqh).
The technical definition of a pillar (rukn) is something that, if it is missing, then whatever it holds up is broken. Similarly, these five pillars are the foundational basis of Islam, like pillars of a building.
Also, there is a hadith of the Prophet Muhammad (peace be upon him) which mentions that "Islam was built upon five (pillars)." [Collection of 40 hadith by Imam Nawawi]. In this hadith, the wording use directly implies building pillars.
Just to be clear, the five pillars are:
- Belief in Allah (and generally: the revealed books, the angels, the prophets, the Day of Judgment, etc.)
- Praying five times a day at specific times and in a specific format
- Giving 2.5% of savings to the poor
- Fasting in the daytime in the Islamic month of Ramadan
- Making pilgrimage to Mecca to perform the rights of Hajj (pilgrimage)
If someone is missing one of the middle three pillars, then their Islam is deficient (incomplete). Technically, it means that they are sinful for not doing that action.
If someone is missing pillar #1 (belief in Allah) -- for example, denying the existence of God -- they may or may not be Muslim. It depends on the severity of the belief.
The final pillar (Hajj) is contingent on you having the means (physical and financial) to go.