To transport digital signals efficiently (i.e. to squeeze as much as possible data bandwidth into as narrow as possible frequency channel), a process called modulation is used. You convert groups of bits into analog combinations of signal frequency, phase, and/or amplitude. The more different, mutually distinguishable combinations of phase and amplitude (called symbols) you use, the more efficient the data transmission is for the same symbol rate, because you can transport more bits at a time per single symbol.
Nowadays, mostly N-QAM modulations are used, which use N symbol “positions” encoded as signal amplitude and phase. 4 QAM has been developed first so it is called just QAM. It uses four symbols so it can carry 2 bits per symbol; in addition to that one, 16 QAM, 64 QAM, and 256 QAM are used in today’s mobile networks, which carry 4, 6, and 8 bits per symbol, respectively.
A distortion of the signal leads to possible confusion of similar symbols at the receiving side. To allow correct decoding, the useful signal must be stronger than the mix of all foreign signals by a particular margin; the higher the number of different symbols used, the smaller the difference between similar ones, hence the higher this margin has to be.
The distortion is caused mostly by foreign signals being mixed with the useful one. One source of such a foreign signal is the thermal noise of the input amplifier at the receiving side, another source are signals sent by other sources in the same frequency channel which reach the receiver - typically, signals from other base stations, called interference. The margin between the useful signal and the foreign ones is normally known as Signal to Noise Ratio, SNR, but the mobile industry has coined a more precise term, Signal to Interference plus Noise Ratio, SINR.
So at the receiving side, the strength of the received useful signal alone (Reference Signal Received Power, RSRP) is not sufficient to assess the reception quality; the SINR is the actual criteria. In crowded urban environments, base stations using the same channels are closer to each other than in rural areas, so the signal from “wrong” stations is relatively stronger at the receiver, hence you need a stronger useful signal to get the same SINR you can get in rural areas from a weaker useful signal, as there the only source of interference is the thermal noise.
Research has shown that it is more efficient to send the data using a more efficient modulation and add some amount of redundant information to them, and let the receiver use that redundant information to correct symbol decoding errors, than to switch to more robust and less efficient modulation immediately. Hence the transmitter chooses among the four modulations above (QAM, 16 QAM, 64 QAM, 256 QAM), and for each of them, it can select from a number of redundancy schemes. The more redundant bits you send, the more errors the receiver can correct, but the total throughput of the original data decreases with the amount of redundant information added.
So for each SINR value, there is a combination of modulation type and redundancy ratio (Modulation and Coding Scheme, MCS) which allows to recover the original data without errors. The receiver tells this to the transmitter using the Channel Quality Indicator (CQI) value, and the transmitter uses that information to choose the corresponding MCS for data sent to that particular receiver.
There is a table for the CQI meaning, e.g. here, and a blog post summarizing the meaning of the abbreviations.
