The acronym SIM stands for Subscriber Identification Module. A SIM is used to authorise a subscriber to access a mobile network. SIMs can come in many form-factors, including cards and chips.
Any device that wants to communicate using a cellular network needs to demonstrate that it is authorised to do so: that its owner is one of the network provider's customers, or of another provider that has a roaming agreement with the home network. The SIM in the device contains the information used to grant — or reject — access to the network.
All SIMs are microchips. Most are embedded in a small plastic card, of which there are four sizes: standard, mini, micro, and nano. Large, credit card-sized standard cards aren't generally used these days, but you will almost certainly have taken one of the smaller cards out of a larger one to slot into a phone or tablet.
Some device have built-in SIMs, which are just SIM chips mounted on the device's circuitboard. This is known as the 'MFF2' form-factor.
Originally, SIM hardware and software were considered a single entity. Nowadays, the SIM functionality is an application running on more general purpose hardware called the UICC, or 'Universal Integrated Circuit Card'.