The odds are what gamblers consider when they bet. In thoroughbred racing, for instance, horses are given odds, or a rating of how they are predicted to win. For instance if a horse has a 20-1 odds, the better will win $20 for every $1 bet. This also means that the horse does not have a very good chance of winning the race. Odds are calculated on a horse depending upon its condition and previous wins. When a racehorse who has great odds such as 20-1 wins a race, he has beat the odds.
The figurative meaning of this phrase, then, means that someone succeeds or survives despite all the logical and calculated impediments to his/her success or living.
To me, this means that when it seems a task that lies before one shows all the signs of being impossible to accomplish, when an obstacle gives every indication of being to enormous to overcome, someone is able to accomplish what had seemed out of the realm of possibility. We hear this kind of thing when women get jobs generally given to men (sports announcers, for example); when an individual overcomes a rare or generally fatal form of cancer; or, when someone (especially a child) is missing for an extended period or exposed to the elements defying the chance of survival, and he/she comes through. Beating the odds smacks of "miracle" for me because it's almost as if something supernatural takes place that makes the human race stop and take note, to say..."What a miracle!" It's when there is no hope, but hope comes through.
To me, beating the odds is a contest. In a contest, such as a game of chance, there are odds of winning and odds of losing. When you actually get into calculating odds, it can be quite complex. Basically we are talking about probability. When we use this idiom, we are often talking about people who had great hardships in their lives, such as poverty or cancer, that they had to overcome. Since most people are not successful at overcoming those situations, we call those that do “beating the odds” and winning.
For more about how odds are calculated, see here:
For more about idioms, see here:
I think of the young people I have taught, almost all from demographics that have historically underachieved, who went on to success in college and beyond. The statistics say that they are far more likely to go to prison than college, but I know many who have overcome the crushing socioeconomic barriers that lay behind these numbers.
"Beating the odds" means someone has shown the determination to keep working and striving to accomplish some end goal in spite of what appear to be overwhelming factors weighted against that outcome. Someone who has beaten the odds has achieved something, and the achievement is noteworthy because many other people would not have had the tenacity to stick with it until the goal was completely reached.
There is an element of perseverance in this phrase, for me, implied in the idea that the obstacles/odds come first and the success/overcoming comes second.
If a person is aware that the odds are stacked against him, yet he tries anyway, he has demonstrated a willingness, perhaps a special willingness, to strive against opposition, to persevere.
"Beating the odds" means to me that an individual or a group of individuals have found a way to circumvent the prevailing wisdom and expectations--even if thought wrong for trying to go against these norms--to circumvent (i.e., get around or past) the prevailing limitations and restrictions in place from any source, be it psychological, spiritual, religious, governmental, cultural, or societal, in order to attain some significant goal that is important to an individual, a group, a habitat or any entity or ideal or concept or event.
By this definition, Jackie Robinson beat the odds by breaking the sports color line; Beethoven beat the odds by composing while deaf; a mother remaining cheerful for her children while undergoing devastating medical treatment or recovering from trauma has beat the odds; Slow Food hopes to beat the odds by reclaiming a pure form of food free of body and cognition altering toxins; some species have beaten the odds by being brought back from near-extinction. You might say I think "true grit," on someone's part, is an integral part of beating the odds.
I think that it goes beyond its literal meaning.
Literally, I "beat the odds" to get the job I have because there are millions of teachers in the US and only one can have my exact job. But we wouldn't really use that phrase in my case.
The idiom means that someone has overcome great difficulties to accomplish something. People who beat the odds are ones who do things like overcoming childhood poverty to become extremely successful.
Beating the odds means that a person found a way to accomplish their goal despite being in a situation where most would consider success unlikely. To put it another way, most people would fail at a certain task, but sometimes people "beat the odds" and find a way to be successful.