Digital mode is a form of communication by converting audio into binary 1 and a 0 or combination of 1 and 0, 1 usually reprensents a high state and 0 represents a low state, sometimes this can be a voltage of say +5 volt for a 1 and lower than +5 volt for 0.
In soundcard modes usually we are dealing with audio tones modulating the radio into a SSB on a radio.
CW is simple data mode of off and on carrier or any other words on and off sounds , combination of off and on sounds , represent a certain letter , certain length of tones represent a letter like in Dit and Dah sound for example E is dit sound T is a Dah sound ,a Z is Dah Dah dit dit , a W is dit dah dah sound. These sounds are translated by the ear or software into text Ham operators know what the Morse code standard Alphabet is and can translate it by ear into something usuable.
The 1 and 0's are coded in such a way as simple idea of a data mode : 500hz tone could represent a 1 and 1000hz tone represents a 0. This example might be model for a FSK like mode, just using two tones , Now say I use tones of say 500, 500, 1000, 500 hz tones it could represent 1101 binary number ,say this binary represents a letter A Now if I use say 500,1000,500, 500hz tones 1011 this could represent a E for example.
In theory you could have many combinations of 1's,0's representing any text out there.
In Date mode it is a little more complex than this , but all data modes have one thing in common they all are using combinations of 1 and 0 to translate into a text or a picture.
Some modes use a Standard for text alphabet such as ASCII , Baudot or Varicode (so everyone knows what binary combination goes with what letter, very useful to know if your designing a digital mode) ,some use a non standard Alphabet coding for specific need or efficency .
Some digital modes use a FEC (forward error correction) in simplisticity terms meaning it is sending the information at least twice. (this is like trying to communicate with some one a long way a way from you by shouting everything twice)
Some digital modes use Interleaving in simplisticity terms is sending information at different parts of the transmission (sending information at different parts of a communication helps to insure the the data does not get corrupted by noise)
Some modes use flip of phase of signal to represent 1 and 0's
Some modes have more than two tones, some use multiples of carriers carrying 1 and 0's
Some mode purposly use small bandwidth to acheive a higher signal to noise ratio , by compacting all the energy into a small package instead of spreading the energy across a large bandwidth , the larger the bandwidth the more it will blend into the noise making it harder to detect a weaker signal.small bandwidth is a cost of speed there is always give and take
Some modes use special mutiple tone shifting to add more information into a small space of time, some mode use certain tones to represent different combinations of 1 and 0's
With a complex scheme for 1 and 0 a computer can figure out these complex schemes to be translated onto your screen as text at a very high speed. The software already knows the mode setup of the mode and knows how to translate it , but if the software does not have a certain mode, it will not know how to decode it, so it is important to have software that can decode the mode.