Can you tell me what a independent contractor is?

I would recommend reading the IRS rules.  The fact that you are being offered an hourly rate and will get raises sounds like a JOB as an EMPLOYEE, not as a contractor.  The hourly rate is bothersome.  An IC would set the rate per house, not per hour and you can say yes and send someone else to do the work.

As a contractor, you buy the supplies and subtract them from your revenue before calculating taxes.  If you spend $20 on paper towels, sponges, 409, etc, your income just went down $20 and you will need to keep the receipts to prove you spent the money.

The general rule is that an individual is an independent contractor if the payer has the right to control or direct only the result of the work and not what will be done and how it will be done. The earnings of a person who is working as an independent contractor are subject to Self-Employment Tax.

The biggest shock most independent contractors suffer is at tax time when they find out they should have been setting money aside and paying quarterly to the IRS and state. Even if you're at a low marginal rate like 10%, add another 5% at least for state, and 15% for self-employment tax (an independent contractor's means of paying social security and Medicare tax), that's a minimum of 30% of your net profit.

When you're an employee your employer withholds amounts for federal and state taxes along with social security and Medicare and also pays half of SS and Med. When you're an independent contractor you need to send that money in yourself.

An independent contractor isn't covered by workers compensation and won't qualify for unemployment benefits.

Get everything set up from the start or you'll get nasty surprises at tax time. It's common for a new independent contractor to owe thousands of dollars in tax on April 15th, plus owing a bunch for the first quarter installment of estimated taxes on the same day.

Being an independent contractor means you are a small business owner.

In this situation, you will own a cleaning service.

Like any cleaning service, you will buy your own cleaning supplies.  These will be business expenses for you.

The company that provides you the houses to clean are a referral service and will pay you for your work.

An independent contractor is essentially a self-employed individual who is contracted to perform work for another entity. You are not an employee, you are responsible for filing your taxes quarterly, you pay for your own benefits and supplies.

You will be self employed, and do your own taxes. You may as well start your own business instead of being dictated to by someone else.

As an independent contractor, you get NO employment rights or benefits. You are personally responsible for any damage or harm you cause. They are not obliged to give you any work. In theory, you are free to negotiate a better rate of pay. In theory, you can refuse any work you don't want but, in reality, if you do, they will simply stop offering work.

The reference to supplies you buy being 'written off' is not meaningful. It needs to be made clear WHO pays for supplies.  Do you have to buy them and then claim the money back? If so, how quickly will they repay you?  Do THEY buy supplies for you and bear the cost directly? This needs to made clear up front.

Who pays for your transport costs to jobs? Does this come out of your $14/hour? Do you get paid for travel time? If you were an employee, you would be on the clock and getting paid for ALL your time related to the job.

In normal practice, you would be an employee with full employment rights and benefits. By giving you the option to refuse jobs, they are hoping this is enough to stop you being legally an employee. It is a way of shafting you while they make a nice living off your efforts without them carrying any risk or long term responsibilities. 

A job is a job. If you really need it, it is better than the alternative. It is not a deal I would enter into unless I had absolutely no choice.

You buy the supplies and it's gets written off as a taxable expense. You are probably getting less than half or about half of what she is getting paid for the work. Don't expect more than $16 an hour after any raises, and since it's cleaning vacation rentals, don't expect a livable income.