There are two separate issues here. Firstly Apple denies that it is infringing any of Nokia's patents and denies that any of them are essential. It notes that if the court does construe the patents as essential then Nokia has failed to license those patents on a FRAND (fair, reasonable and non-discriminatory) basis. Nokia has offered licensing terms to Apple, but Apple feel that they are unreasonable (i.e. do not fall into the FRAND criteria).
Secondly Apple has alleged that Nokia has infringed some of Apple's own patent in creating some of its recent devices. The Nokia 5310, E71, Nokia N900 and carbide.c++ (Nokia's developer tool) products are mentioned by name, but some of the infringements could, allegedly, apply to all USB devices, or all Symbian, S60 and Series 40 devices.
Patents claims are complex legal areas and this dispute is likely to continue for some time. Counter-suits are common in patent disputes as they can be employed as negotiating tactics. In all likelihood this will still be settled out of court. With Nokia's original filing the general consensus amongst analysts, legal and other commentators (e.g. see Engadget's breakdown here) was that Apple did have a case to answer. It is worth noting that Apple's alleged infringements of Nokia patents are in fields that are deemed as essential to industry standards, somewhat in contrast with Nokia's alleged infringements of Apple's patents.
In a press release about the filing Apple used some concise but dramatic language:
"Other companies must compete with us by inventing their own technologies, not just by stealing ours,” said Bruce Sewell, Apple’s General Counsel and senior vice president."
Apple uses similar language in the filing itself:
"In 2007, Apple introduced the iPhone a ground-breaking device that allowed users access to the functionality of the already popular iPod on a revolutionary mobile phone and Internet device... The iPhone platform has caused a revolutionary change in the mobile phone category.
In contrast, Nokia made a different business decision and remained focused on traditional mobile wireless handsets with conventional user interfaces. As a result, Nokia has rapidly lost share in the market for high-end mobile phones...
In response, Nokia chose to copy the iPhone, especially its enormously popular and patented design and user interface."
Source: Digital Daily, Court filings