An auditor is an independent third party (neither a member of the company's management nor an owner of the company) that reviews the financial statements prepared by management and provides an opinion regarding their accuracy and fairness.
Definition of the word qualification: A statement or assertion that makes another statement or assertion less than absolute. Example: The Mets are great fielding team except for the fact that they can't catch. The part after "except for" is a qualification of the statement "The Mets are great fielding team".
Unqualified: The auditor says the financial statements and related disclosures are free of material misstatement and fairly present information. [01]
Unqualified with explanatory paragraph: Unqualified opinion with an additional paragraph noting something important (like the company might go bankrupt within the next year).
Qualified: Issued when the auditor was prevented from doing work in certain areas (called scope limitation). Also issued if the company doesn't follow GAAP for something but the departure from GAAP is not serious enough to affect the fairness of the financial statements overall.
Adverse or disclaimer: Issued when there is a problem with the financial statements (e.g., there is a material misstatement or they don't conform to GAAP). A disclaimer happens when the auditor feels it was unable to gather enough evidence to form an opinion.
By far, the most common type of audit opinion is unqualified. Think about it from the company's perspective. If the auditor has a problem, the company will make the adjustments deemed necessary by the auditor. After all, the company does not want the auditor to issue something other than an unqualified opinion. So typically the auditor will find issues, the company will correct them, the auditor will be OK with the financial statements after the corrections and issue an unqualified opinion.