Oh boy, a thorough understanding will be difficult, because reading these things to their full potential can take 10+ years of experience... If you really want to dive into it, read a book on seismic (exploration) geophysics -- this is the main reference book in the field: https://wiki.seg.org/wiki/Seismic_Data_Analysis .
The best way to understand the picture is to understand how the data came to be:
The subsurface consists of layers (and other shapes) of varying density and compressibility, leading to different wave speeds. For example, mechanical vibrations (=seismic waves) move with a different speed through sand than through granite, ...
Take a famous model, the Marmousi model:
This model has variations in the velocity (low velocities at the top, faster towards the bottom), with all kinds of geological features: faults, folds, uncomformities, ...
The seismic company creates an explosion to create a seismic wave that propagates through the model, and at every interface where the seismic properties change (called the 'acoustic impedance'), a reflection is created. However, the company only records the signal at the top, the same level where it created the seismic wave:
https://www.youtube.com/watch?v=U0hT9vO_oHA ; on the left you see the wave move into the Marmousi model, reflecting off every impedance change; on the right you see the data that is recorded at the receivers, with the color specifying a contraction or an extension (any wave creates both extension and contraction, never just one: https://www.youtube.com/watch?v=2rYjlVPU9U4 )
Actually, the recording consists of individual receivers which record individual traces, it's just interpolated and turned into a black-and-white image in the video:
Eventually, through careful and computationally intense algorithms, the recorded data is turned into a stack and is 'migrated', such that the recorded data is 'imaged' at the approximate location of the reflections in the subsurface. When still using the individual traces you get:
The traces are now SO close together that it almost becomes a black and white image. And this is where the colors come in, the same section may be displayed as:
where the positive (right-ward, black) trace has been replaced with RED, and the negative (left-ward, white) move of the trace has been replaced with BLUE, and white as the intermediate color.
So, for the Marmousi model, people can make these type of images:
you see how it looks similar to the true model -- but is still generally much noisier, particularly for deeper reflections further down the image? In principal, the red/blue color corresponds to an increase or a decrease in acoustic impedance, but it's sometimes tough to see these things clearly...
Hence, the image that you have is probably a migrated stack, varying from extremely light blue to dark blue to grey to red to yellow. The z axis corresponds to (approximate) depth, the x axis corresponds to receiver positions/offsets. All the lines are contrasts between rock types that have been geologically deformed, either a positive or negative impedance contrast. Features of interest to geologists are too numerous to mention, but of basic interest are (1) tracking a whole line over the entire image to see the continuity of a single reflecting unit, (2) seeing a fault -- where a reflector breaks and picks up a bit below, (3) finding really intense ('bright') spots in the data, (4) finding salt, e.g., as done here https://www.kaggle.com/c/tgs-salt-identification-challenge/ ...
But yeah, demand more information from whoever wants you to do this work about what features are of interest because there's too much in the image to just blindly start learning things...