@joe-c is right they do keep the leadership informed of concerns. They have a number of roles:-
- Get to know individual legislators and what motivates / interests them
- Identify bills or points that are problematic
- Try to come up with solutions to get bills through
Parliamentary arithmetic will dictate how important their role is and how much the whips will offer for a vote - a close vote on a critical issue may see lots of incentives.
Sometimes it's quite straightforward - if 50 legislators say a bill with a phase-in of 1 year is too short but they would vote for a phase-in of 3 years then that change will likely be made.
Other things they can do is offer subsidies or one-off payments for particular companies e.g. if widget X is to be banned an incentive of £100k for companies to change their factories to widget Y.
Sometimes the incentive might be as small as for the Government Minister to acknowledge a specific local issue in a debate perhaps in response to a staged intervention (i.e. this is all lined up beforehand), e.g.
Govt Minister: I will give way to the Member for Littlehampton.
Member: In my constituency Acme Ltd make 40% of the world supply of
widget X can the minister assure me there will be financial support
for companies like Acme Ltd.
Govt Minister: I am delighted to inform the house that there will be a fund to give grants of up to £100k to companies like Acme to update their factories.
This then allows the individual member to demonstrate to his constituency how he is working for them.
Other incentives the whips can give are promotions to government, places on committees, visits by Cabinet ministers to their constituency, even places on overseas trips.
On the negative side as well as not giving the above (!) the ultimate sanction they can take is to "withdraw the whip", this means the legislator will not receive any guidance on which votes are important, how they are encouraged to vote. Ultimately someone without the whip cannot stand for that party at the next election. Whips have a lot of "soft" power backed up by the ability to effectively end an individual's political career.
See Wikipedia's article: "September 2019 suspension of rebel Conservative MPs"
On 29 October 2019, 10 of the suspended MPs had the whip restored. Six stood down at the December 2019 election, while four contested it as Conservative candidates; all four retained their seats. Of the 11 who remained suspended, six declined to stand at the election, while five stood as independents or Liberal Democrats; all five lost their seats.