Update 19 July 2015

In April 2015 new visitor rules activated as a result of the on-going Simplification Project. The text cited below was replaced with text that makes the rules easier to understand. The new rules are at Appendix V, and the operative text is in Paragraph V 4.2 (e).

...must have sufficient funds...

Simpler. Easier to understand. But a whole lot more nuanced and subtle...

The press release is at Changes to the UK's Visa Services.

All of the same principles put forward in the original answer still apply, and decision-makers still use the same criteria to assess an applicant's credibility.

Original Answer

Your bank accounts suggested that you were using a 'funds parking' strategy, and the ECO challenged your credibility as a result; hence a refusal. They also consider the parking strategy to be a mild form of deception, which commensurately damages your credibility.

Briefly, the 'funds parking' strategy involves having a friend or relative inflate your account by giving you a temporary loan which you repay after the visa has been issued. But when they detect this strategy, they are entitled to refuse on Paragraph 41 (vi), which says in part

will maintain and accommodate himself and any dependants adequately out of resources
available to him

with emphasis on 'available to him'. You used your mother's bank account, which defies this rule in the first instance because you need to show the funds are available to you. Had they wanted to, they could have refused on that ground alone. Those arrangements need to be rigorously explained.

In your case, the irregular deposits came from transferring funds from another account which belongs to you. This can be overcome by simply including an explanatory note along with the other statements such that the debits from one account agree with the credits in the other account. This makes the provenance of the funds clear.

In the comments below your question, you ask if you should compound the problems by lying. At the moment, your history now contains a refusal suggesting credibility issues. If you get caught lying in a subsequent application, your credibility will be further damaged. If and when your credibility becomes depleted, you will be locked in to refusals on that ground alone.