Due to the subtle blurs and fading opacity it is highly doubtful this was created in Illustrator.
It's most likely a Photoshop project. I only mention this due to the question tags. Trying to pull off such an image in Illustrator would be a lesson in frustration more than anything. It could possibly be done via gradient meshes, opacity masks, etc.. but I'd not want to tackle that project unless I was being paid very well for it.
Text can be easily distorted by using the Displacement Map feature within Photoshop.
Displacement maps distort one layer based upon a greyscale "map". The map is essentially a greyscale image which is used as a sort of topography for distortion, white areas are seen as "high" and black areas are seen as "low". Grey area are transition regions between the two.
Essentially, you'd set the text up straight, create a greyscale image for the map, then use
Filter > Distort > Displace to distort the text with the map...
It can take considerable effort to create a displacement map which distorts in a manner you want.
In the particular sample in the question, chances are high that there was some additional processing after using the Displace filter, such as reducing opacity, blurring, and other filters used such as the Maximum/Minimum filters.
There are hundreds of online tutorials if you merely search for "Photoshop Displacement Map". Here are just a few top hits...
I have no affiliation with any of the links. They are merely added here for ease.