What does "bids" mean in this sentence?

The children would be attempting to obtain their parents' attention. A bid can be an attempt to secure some objective.

Donald Trump's bid to overturn presidential election stumbles as judge dismisses Pennsylvania lawsuit

Daily Telegraph

US election 2020: Joe Biden’s £600m presidential bid fails to secure an easy win over Donald Trump

iNews (UK)

A British transgender man’s bid to be named the father rather than the mother on his child’s birth certificate has been rejected by the country’s highest court, in a case that has highlighted evolving conceptions of gender.

Reuters

bid noun [C] (ATTEMPT) C2 an attempt to achieve or get something:

Bid (Cambridge Dictionary)

Making a bid for something is an attempt to solicit a particular type of behavior from someone else. For example:

"The company bids on the government contract."

Means that the company applies to receive the contract. It does NOT mean the company is bribing a government employee with money!

As an extension of this meaning, a person can "bid" on an item, and offer "consideration" (money) as one part of the bid. However, the bid must typically be "accepted" before it is valid. The point here is that simply offering the highest amount of money is not sufficient to win an activity that involves bidding; it is only one aspect of a subset of completed bids. For example, on auction sites such as eBay, valid bids would also require a user account in good standing and generally a mailing address. In other places, bids may have more substantive requirements.

To "bid for attention" is a common phrase, particularly when used regarding a child's behaviour. It's really being used in the same way as a monetary bid for goods - the child in this case is making a bid by asking for the attention of the parent, and the parent can decide whether to accept the "bid" by giving attention or not.

This article may help give more context.