Hobby is an activity where primary motivation for engaging into activity is to have fun, not to make profit.
Hobby expenses might be deductible. If hobby producing income, then one can deduct expenses associated with a hobby up to the amount of the income; however, a taxpayer cannot carry forward the deductions. Meaning if expenses are $5000 and income earned from hobby $1000, one can deduct $1000 in expenses, but remaining $4000 will be lost and cannot be carried over to future years. Another thing to remember, that one can deduct hobby expenses only if he/she itemizes instead of taking a standard deduction and hobby deductions are subject to 2% AGI limit.
As far as tax law if the activity shows profit for 3 out of 5 years, activity is considered to be engaged in for profit and treated a business.