Large carious lesions can cause a tooth to ache. Often patients report their tooth starts to hurt after eating. This is probably due to the bacteria in a carious lesion being fed by the food that a person eats. The bacteria in the process of metabolizing the food will produce acidic substances(lactic acid) and these may irritate the pulp of the affected tooth. Often these aches are transient and will come and go.
If a deep carious lesion is cleaned out carefully by a dentist and no obvious pulpal exposure occurs, the dentist can place a sedative or cement filling in the affected tooth and it may become comfortable. If the tooth is properly sealed the pulp may be allowed to recover and the tooth may become a "happy" tooth.
Of course some teeth with deep caries do require root canal since their pulps have been irreversible damaged. If after having a sedative filling has been placed in a deep lesion, the tooth continues to throb or ache,then an endodontic procedure is usually indicated. The sensitivity is coming from the tooth's pulp and removing it with a root canal will usually make the tooth comfortable.